Wednesday, July 13, 2011

Relationships in the math

The Math puts into practice a lot of my earlier articles on game design theory but I think the most important in understanding the indifference line (and part two of that article). I would like to better explain the how and why of that statement here and now.

The reason people invent sub-games like E6 is twofold.  One is to parse out those higher level powers that make basic adventure tropes not work like scrying, teleport, and so on. I answer this with my argument on favorable system assumptions. The second reason for things like E6 is to hold onto the early magic of the game for as long as possible. When you first sit down to make a character, you are faced with such fundamental tradeoffs. Do I want a higher dexterity or strength? Should I take power attack or expertise? They are simple decisions that feel like they craft an entirely new character with each choice and shape your vision into reality.

And at low levels they are legitimate tradeoffs. Sure some are better than others, but for the most part they are all reasonable character choices that distinguish the character from others. This is because game designers design the game predominantly for low levels. That is where the game is simplest so that is where it is simplest to design. People generally start at low levels, so that is where you have sell them on the game. There are so many moving pieces at high levels that you can’t be confident in balance anyways, so it gets less attention. I’m not saying it gets no attention, but it definitely gets less. Most games are brilliantly fun at low levels and break down at higher levels.

The reason is that the relationships at low levels are not the same relationships at high levels. This is fine so long as you don’t try and have low level relationships interact with high level relationships. Unfortunately, that is sort of the point of RPGs; have a character progress through levels and attain wealth and fame. To demonstrate this change, consider the basic question of +2 atk or +2 dmg on the indifference line. First consider it at 10 expected damage with a 50% to-hit rate. They are equally valid strategies. Then consider it at 20 expected damage with a 50% to-hit rate. Attack is twice as powerful as damage.

Alright, so then what’s the solution? Well, you need the relationships to evolve across levels as well. Fourth edition sort of tried to achieve this by having things scale by tier. At level 21, your at will does an extra d6. The main problem with it is that it scales in big lumps. If the +1d6 was enough to balance it all the way to level 30, then was it overpowered at 21? And if not, how underpowered was it at level 20?

The better solution is to have things progress linearly across levels in smaller bites. It gives more opportunities to make the players feel like they are improving and provides a more stable progression. The problem with linear is that table-top RPGs require simple numbers. If the math wants you to increase by 1.42 per level, you probably gotta pick between 1 or 2 with maybe being able to finagle a 1.5 (but even this sometimes feels weird). Linear integers don’t provide enough nuance to represent the evolving relationships over time.

My solution was to discount the integers such that while the player experienced the whole integers, the math experienced incremental difference between the integer and some different integer that increased at a different rate. In this way, nice whole numbers have the impact of increasing at halves, thirds, quarters, or even fifths depending on the rate at which other things increased in other places. Here is a hypothetical example:

We see that the incremental benefit and the straight benefit both bring the game to the same numerical plus (the red line). But when we look at *only* the incremental portion of the incremental benefit (the area labeled ‘B’), we see that they actually progress very differently. At low levels, when the game is at that point of the indifference line where tradeoffs are about equal, the incremental and the straight benefit are about equally rewarding. But as we progress in levels, the straight benefit rises at a much faster rate. In this hypothetical, the incremental bonus would be a bonus to attack and the straight benefit a bonus to damage. Now think back to the +2/-2 discussion above. At low levels, they are equally valid, but at higher levels, the damage-option has to be more rewarding than the attack-option for the game to remain balanced.

In this way, the fun decisions at level one (“I want to hit hard!”) are still valid at level 15 and the relationship organically evolves. We don’t need some gimmick or math fix to rebalance the game. More importantly, *during the game* your decision remains the same basic decision it was at first level. You decide if you want to apply power attack or not. During play, it maintains the simple elegance it had at first level.

Or that is the hope anyways….

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